When I was discovering jazz as a student, Thelonious Monk seemed to epitomise the artistic originality, indifference to rules and guileless eccentricity (he liked weird hats, and was given to shuffling dances onstage) that I loved about the music. Monk's piano solos clanged with dissonance, bumped along in hopping runs or glowered with baleful silences, and his astonishing compositions (now recognised as modern musical landmarks, regardless of genre) had a strange, inelegant beauty that brusquely reinvented what melody, harmony and rhythm could mean.

Brilliant Corners, recorded for the Riverside label in 1956 with an A-list band including saxophonist Sonny Rollins and former Charlie Parker drummer Max Roach, was the most compositionally ambitious session in the former church pianist's decade-long jazz career thus far. In a legendarily fractious session, the title track's growling theme was so treacherous in its lurching phrasing and abrupt time changes that a band this good still spent 25 takes on it, and the final version was only possible by splicing two takes together. But Brilliant Corners was no calculated technical highwire act, but a piece of audaciously adventurous composing that has never lost its power to startle and seduce over the decades.

From Monk's opening stabbed chords (as if he were chipping rock) to the bone-shaking notes, guttural horn harmonies and sudden thematic gallops, Brilliant Corners is gripping – as are the composer's jangling improvisations, and Rollins's lazily unfolding and huge-toned tenor solo. The session's full of captivating variety too – from the urban graininess of Hornin' In to the relaxed groove of Let's Cool One, the surreal mix of Monk's chordal bluntness and the coyness of a glockenspiel on Pannonica to the bleary rootsiness of the wonderful blues Ba Lue Bolivar Ba Lues Are. Arriving just before the late-50s free-jazz upheavals of Ornette Coleman, John Coltrane and Cecil Taylor, this was music that showed just how powerfully song-form harmonies and the tempered scale could be wrenched into new shapes.

Or you could simply star rate it, or add it to one of your album lists. There are more than 3m new pages for you to explore as well as 600,000-plus artists' pages – so if, for example, you prefer your jazz to come in the shape of, er, The Shape of Jazz to Come, or think a better choice is John Coltrane's A Love Supreme, then find their albums and get to work …

Continuing our new series in which Guardian and Observer writers pick their favourite albums ever – with a view that you might do the same – Kitty Empire hails some casual sexism and eye-rolling double entendres. Oh, and those riffs ...